and let us first remark, that _e_X′, _e_Y′, _e_Z′ are the components of the ponderomotive force acting upon the electron, and are considered in a moving system which, at this moment, moves with a velocity which is equal to that of the electron. This force can, for example, be measured by means of a spring-balance which is at rest in this last system. If we briefly call this force as “the force acting upon the electron,” and maintain the equation:— Mass-number × acceleration-number = force-number, and if we further fix that the accelerations are measured in the stationary system K, then from the above equations, we obtain:— Longitudinal mass: $$ \frac{m}{(\sqrt{1 - \frac{v^2}{c^2}})^{\frac{3}{2}}} $$ Transversal mass: $$ \frac{m}{\sqrt{1 - \frac{v^2}{c^2}}} $$ Naturally, when other definitions are given of the force and the acceleration, other numbers are obtained for the mass; hence we see that we must proceed very carefully in comparing the different theories of the motion of the electron. We remark that this result about the mass hold also for ponderable material mass; for in our sense, a ponderable material point may be made into an electron by the addition of an electrical charge which may be as small as possible. Let us now determine the kinetic energy of the electron. If the electron moves from the origin of co-ordinates of the system K with the initial velocity 0 steadily along the X-axis under the action of an electromotive force X, then it is clear that the energy drawn from the electrostatic field has the value ∫_e_X_dx_. Since the electron is only slowly accelerated, and in consequence, no energy is given out in the form of radiation, therefore the energy drawn from the electro-static field may be put equal to the energy W of motion. Considering the whole process of motion in questions, the first of equations A) holds, we obtain:— $$ W = \int eXdx = \int_0^v m\beta^3 vdv = mc^2 (\frac{1}{\sqrt{1 - \frac{v^2}{c^2}}} - 1) $$ For _v_ = _c_, W is infinitely great. As our former result shows, velocities exceeding that of light can have no possibility of existence. In consequence of the arguments mentioned above, this expression for kinetic energy must also hold for ponderable masses. We can now enumerate the characteristics of the motion of the electrons available for experimental verification, which follow from equations A). 1. From the second of equations A), it follows that an electrical force Y, and a magnetic force N produce equal deflexions of an electron moving with the velocity _v_, when Y = N_v_/_c_. Therefore we see that according to our theory, it is possible to obtain the velocity of an electron from the ratio of the magnetic deflexion A_{_m_}, and the electric deflexion A_{_e_}, by applying the law:— $$ \frac{A_{m}}{A_{e}} = \frac{v}{c} $$